Bibas is 100% right.

I have taken 2 months grace period before my OPT start and 2 months after my OPT. International Advisor of some college are saying only 2 months grace period which is wrong.

Also, bibas is right in pointing taking start date of OPT as end of July. That way your 60 days grace period will take you to 1st of October (which is your H1 start date). No hassel for any visa stamping, Kaplan etc.

Thanks bibas for sharing your thought.